U.S. patent application number 11/178999 was filed with the patent office on 2006-10-19 for pulse contour method and apparatus for continuous assessment of a cardiovascular parameter.
Invention is credited to Feras Hatib, Jeffrey Pearce, Luchy Roteliuk.
Application Number | 20060235323 11/178999 |
Document ID | / |
Family ID | 37109466 |
Filed Date | 2006-10-19 |
United States Patent
Application |
20060235323 |
Kind Code |
A1 |
Hatib; Feras ; et
al. |
October 19, 2006 |
Pulse contour method and apparatus for continuous assessment of a
cardiovascular parameter
Abstract
A cardiovascular parameter such as cardiac output is estimated
from a current pressure waveform data set without needing to
directly measure blood flow or arterial compliance. The general
shape of an input flow waveform over one beat-to-beat cycle is
assumed (or computed), and then the parameters of a
flow-to-pressure model, if not pre-determined, are determined using
system identification techniques. In one embodiment, the parameters
thus determined are used to estimate a current peripheral
resistance, which is used not only to compute an estimate of the
cardiovascular parameter, but also to adjust the shape of the input
flow waveform assumed during at least one subsequent beat-to-beat
cycle. Another embodiment does not require computation of the
peripheral resistance and still another embodiment computes a flow
estimate from an optimized identification of the parameters
defining the assumed input flow waveform.
Inventors: |
Hatib; Feras; (Irvine,
CA) ; Roteliuk; Luchy; (Lake Forest, CA) ;
Pearce; Jeffrey; (Sultan, WA) |
Correspondence
Address: |
EDWARDS LIFESCIENCES CORPORATION
LEGAL DEPARTMENT
ONE EDWARDS WAY
IRVINE
CA
92614
US
|
Family ID: |
37109466 |
Appl. No.: |
11/178999 |
Filed: |
July 11, 2005 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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60670767 |
Apr 13, 2005 |
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Current U.S.
Class: |
600/526 |
Current CPC
Class: |
A61B 5/0215 20130101;
A61B 5/02028 20130101; A61B 5/02007 20130101; A61B 5/02108
20130101; A61B 5/029 20130101 |
Class at
Publication: |
600/526 |
International
Class: |
A61B 5/02 20060101
A61B005/02 |
Claims
1. A method for determining a cardiovascular parameter equal to or
derivable from cardiac output (CO) comprising: inputting a current
pressure waveform data set corresponding to arterial blood pressure
over a current pressure cycle; determining defining parameters of
an assumed input flow waveform as a function of a peripheral
resistance value determined for at least one previous pressure
cycle; determining model parameters of a model of a relationship
between the assumed input flow waveform and the current pressure
waveform data set; computing a current peripheral resistance value
as a function of the model parameters; and computing an estimate of
the cardiovascular parameter as a function of the current
peripheral resistance value and the current pressure waveform data
set.
2. A method as in claim 1, further comprising determining the
defining parameters of the assumed input flow waveform also as a
function of shape characteristics of the current pressure waveform
data set.
3. A method as in claim 2, in which the assumed input flow waveform
is a series of component waveforms, with one component waveform per
pressure cycle.
4. A method as in claim 3, in which: the defining parameters
include duration and amplitude; and the duration of the component
waveform for the current pressure cycle is set at least
approximately equal to a time interval between systole onset and
systole in the current pressure waveform data set.
5. A method as in claim 4, further comprising: estimating a
diastolic time constant as a product of a sampling rate at which
the pressure waveform data set is derived and a function of a model
feedback parameter; estimating an arterial compliance value as a
ratio of the diastolic time constant and the peripheral resistance
value; estimating a systolic time constant from chosen points in
the current pressure waveform data set; computing an aortic
characteristic resistance value as a ratio of the systolic time
constant and the arterial compliance value; setting the amplitude
of the component waveform for the current pressure cycle Ito be
inversely proportional to the square of a function of at least one
aortic characteristic resistance value.
6. A method as in claim 5, further comprising: computing the mean
of a plurality of aortic characteristic resistance values, which
will include at least one aortic characteristic resistance value
estimated for a previous cycle; setting the amplitude of the
component waveform for the current pressure cycle to be inversely
proportional to the square of the product of the mean and a
calibration constant.
7. A method as in claim 6, further comprising setting the amplitude
of the component waveform for the current pressure cycle to be
inversely proportional to the square of the product of the mean,
the calibration constant, and the arterial compliance value.
8. A method as in claim 3, in which the assumed input flow waveform
comprises a train of square-wave signals, each forming a respective
one of the component waveforms.
9. A method as in claim 3, further comprising: setting the
amplitude of the component waveform for the current pressure cycle
to be proportional to a peak-to-peak value of the current pressure
waveform data set and inversely proportional to a function of the
current peripheral resistance value.
10. A method as in claim 9, further comprising: determining a mean
value of a plurality of previously estimated peripheral resistance
values; and setting the amplitude of the component waveform for the
current pressure cycle to be proportional to the peak-to-peak value
and inversely proportional to the mean value.
11. A method as in claim 10, further comprising: determining a
calibration constant; and setting the amplitude of the component
waveform for the current pressure cycle to be proportional to the
peak-to-peak value and inversely proportional to the mean value
scaled by the calibration constant.
12. A method as in claim 1, in which: the model is a discrete,
auto-regressive representation of a multi-element Windkessel model
of the aorta; and the model parameters are coefficients of the
discrete, auto-regressive representation.
13. A system for determining a cardiovascular value equal to or
derivable from cardiac output (CO) comprising: an arrangement
generating a current pressure waveform data set corresponding to
arterial blood pressure over a current pressure cycle; a processing
system including: an input flow waveform generation module
comprising computer-executable code for determining defining
parameters of an assumed input flow waveform as a function of a
peripheral resistance value determined for at least one previous
pressure cycle; a system parameter identification module comprising
computer-executable code for determining model parameters of a
model of a relationship between the assumed input flow waveform and
the current pressure waveform data set; a model parameter
computation module comprising computer-executable code for
computing a current peripheral resistance value as a function of
the model parameters; and a cardiovascular value computation module
comprising computer-executable code for computing an estimate of
the cardiovascular parameter as a function of the current
peripheral resistance value and the current pressure waveform data
set.
14. A system as in claim 13, in which the system parameter
identification module is further provided with computer-executable
code for determining the defining parameters of the assumed input
flow waveform also as a function of shape characteristics of the
current pressure waveform data set.
15. A system as in claim 14, in which the assumed input flow
waveform is a series of component waveforms, with one component
waveform per pressure cycle.
16. A system as in claim 15, in which: the defining parameters
include duration and amplitude; and the duration of the component
waveform for the current pressure cycle is set at least
approximately equal to a time interval between systole onset and
systole in the current pressure waveform data set.
17. A system as in claim 15, in which the input flow waveform
generation module is further provided for setting the amplitude of
the component waveform for the current pressure cycle to be
proportional to a peak-to-peak value of the current pressure
waveform data set and inversely proportional to a function of the
current peripheral resistance value.
18. A system as in claim 17, further comprising: an averaging
module comprising computer-executable code for determining a mean
value of a plurality of previously estimated peripheral resistance
values; in which input flow waveform generation module is further
provided for setting the amplitude of the component waveform for
the current pressure cycle to be proportional to the peak-to-peak
value and inversely proportional to the mean value.
19. A system as in claim 18, further comprising: a calibration
module determining a calibration constant; in which the input flow
waveform generation module is further provided for setting the
amplitude of the component waveform for the current pressure cycle
to be proportional to the peak-to-peak value and inversely
proportional to the mean value scaled by the calibration
constant.
20. A system as in claim 16, in which the assumed input flow
waveform is a train of square-wave signals, each forming a
respective one of the component waveforms.
21. A system as in claim 13, in which: the model is a discrete,
auto-regressive representation of a multi-element Windkessel model
of the aorta; and the model parameters are coefficients of the
discrete, auto-regressive representation.
22. A method for determining a cardiovascular parameter comprising:
inputting a current pressure waveform data set corresponding to
arterial blood pressure over at least one current pressure cycle;
determining defining parameters of an assumed, non-impulsive input
flow waveform as a function of at least one shape-characterizing
value in the current pressure waveform data; determining model
parameters of a flow-to-pressure cardiovascular model; and
computing an estimate of the cardiovascular parameter as a function
of the determined model parameters.
23. A method as in claim 22, in which the assumed input flow
waveform is a series of assumed input waveform components.
24. A method as in claim 23, in which the assumed input waveform
components are chosen from the group of functions comprising square
waves, saw tooth waves, polynomials, piecewise linear functions, at
least one Bezier curve and at least one sinusoidal component
curve.
25. A method as in claim 22, in which the cardiovascular parameter
is blood flow.
26. A method as in claim 22, in which the cardiovascular parameter
is cardiac output.
27. A method as in claim 22, in which the cardiovascular parameter
is derivable from cardiac output, the method further comprising
computing a cardiac output estimate as a function of the determined
model parameters as a preliminary computation to computing the
cardiovascular parameter.
28. A processing system for determining a cardiovascular value
equal to or derivable from cardiac output (CO) comprising: an
arrangement generating a current pressure waveform data set
corresponding to arterial blood pressure over a current pressure
cycle; an input flow waveform generation module comprising
computer-executable code for determining defining parameters of an
assumed input flow waveform as a function of at least one
shape-characterizing value in the current pressure waveform data; a
system parameter identification module comprising
computer-executable code for determining model parameters of a
model of a relationship between the assumed input flow waveform and
the current pressure waveform data set; a model parameter
computation module comprising computer-executable code for
computing a current peripheral resistance value as a function of
the model parameters; and a cardiovascular value computation module
comprising computer-executable code for computing an estimate of
the cardiovascular parameter as a function of the determined model
parameters.
29. A processing system as in claim 28, in which the assumed input
flow waveform is a series of assumed input waveform components.
30. A processing system as in claim 29, in which the assumed input
waveform components are chosen from the group of functions
comprising square waves, saw tooth waves, polynomials, piecewise
linear functions, at least one Bezier curve and at least one
sinusoidal component curve.
31. A processing system as in claim 28, in which the cardiovascular
parameter is blood flow.
32. A processing system as in claim 28, in which the cardiovascular
parameter is cardiac output.
33. A processing system as in claim 28, in which the cardiovascular
parameter is derivable from cardiac output, in which the
cardiovascular value computation module is further provided for
computing a cardiac output estimate as a function of the determined
model parameters as a preliminary computation to computing the
cardiovascular parameter.
34. A method for determining cardiac flow comprising: inputting a
current pressure waveform data set corresponding to arterial blood
pressure over at least one current pressure cycle; determining
model parameters of a flow-to-pressure cardiovascular model;
determining the defining parameters of an assumed input flow
waveform by computing a set of the defining parameters that, when
transformed according to the cardiovascular model, most closely
yields the current pressure waveform data set in a predetermined
sense; and estimating the cardiac flow as a function of the assumed
input flow waveform.
35. A method as in claim 34, further comprising estimating cardiac
stroke volume by integrating the assumed input flow waveform over
at least one pressure cycle.
36. A method as in claim 34, further comprising determining the
model parameters separately from the defining parameters of the
assumed input flow waveform.
37. A method as in claim 36, further comprising pre-determining the
model parameters independent of the current pressure waveform data
set.
38. A method as in claim 36, further comprising determining the
defining parameters of the assumed input flow waveform and the
model parameters of the flow-to-pressure cardiovascular model
simultaneously, in a single optimization.
39. A processing system for determining cardiac flow comprising: an
input flow waveform generation module comprising
computer-executable code for inputting a current pressure waveform
data set corresponding to arterial blood pressure over at least one
current pressure cycle; a model parameter computation module
comprising computer-executable code for determining model
parameters of a flow-to-pressure cardiovascular model; determining
the defining parameters of an assumed input flow waveform by
computing a set of the defining parameters that, when transformed
according to the cardiovascular model, most closely yields the
current pressure waveform data set in a predetermined sense; and a
cardiovascular value computation module comprising
computer-executable code for estimating the cardiac flow as a
function of the assumed input flow waveform.
40. A system as in claim 39, in which the model parameter
computation module is further provided for estimating cardiac
stroke volume by integrating the assumed input flow waveform over
at least one pressure cycle.
41. A system as in claim 39, in which the model parameter
computation module is further provided for determining the model
parameters separately from the defining parameters of the assumed
input flow waveform.
42. A system as in claim 41, in which the model parameter
computation module pre-stores the model parameters independent of
the current pressure waveform data set.
43. A system as in claim 41, in which the input flow waveform
generation module and the model parameter computation module are
portions of a single body of computer-executable code provided for
determining the defining parameters of the assumed input flow
waveform and the model parameters of the flow-to-pressure
cardiovascular model simultaneously, in a single optimization.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims priority of U.S. Provisional Patent
Application No. 60/670,767, filed 13 Apr. 2005.
BACKGROUND OF THE INVENTION
[0002] 1. Field of the Invention
[0003] This invention relates to a method for estimating a
cardiovascular or hemodynamic parameter such as cardiac output
(CO), as well as to a system that implements the method.
[0004] 2. Background Art
[0005] Cardiac output (CO) is an important indicator not only for
diagnosis of disease, but also for continuous monitoring of the
condition of both human and animal subjects, including patients.
Few hospitals are therefore without some form of conventional
equipment to monitor cardiac output.
[0006] One basis for most common CO-measurement systems is the
well-known formula CO=HRSV, where SV is the stroke volume and HR is
the heart rate. SV is usually measured in liters and HR is usually
measured in beats per minute, although any other units of volume
and time may be used. This formula simply expresses that the amount
of blood the heart pumps out over a unit of time (such as a minute)
is equal to the amount it pumps out on every beat (stroke) times
the number of beats per time unit.
[0007] Since HR is easy to measure using any of a wide variety of
instruments, the calculation of CO usually depends on some
technique for estimating SV. Conversely, any method that directly
yields a value for CO can be used to determine SV by division by
HR. Of course, estimates of CO or SV can then be used to estimate,
or contribute to estimating, any parameter that can be derived from
either of these values.
[0008] One invasive way to determine cardiac output (or,
equivalently, SV) is to mount some flow-measuring device on a
catheter, and then to thread the catheter into the subject and to
maneuver it so that the device is in or near the subject's heart.
Some such devices inject either a bolus of material or energy
(usually heat) at an upstream position, such as in the right
atrium, and determine flow based on the characteristics of the
injected material or energy at a downstream position, such as in
the pulmonary artery. Patents that disclose implementations of such
invasive techniques (in particular, thermodilution) include: [0009]
U.S. Pat. No. 4,236,527 (Newbower et al., 2 Dec. 1980); [0010] U.S.
Pat. No. 4,507,974 (Yelderman, 2 Apr. 1985); [0011] U.S. Pat. No.
5,146,414 (McKown, et al., 8 Sep. 1992); and [0012] U.S. Pat. No.
5,687,733 (McKown, et al., 18 Nov. 1997).
[0013] Still other invasive devices are based on the known Fick
technique, according to which CO is calculated as a function of
oxygenation of arterial and mixed venous blood. In most cases,
oxygenation is sensed using right-heart catheterization. There
have, however, also been proposals for systems that measure
arterial and venous oxygenation non-invasively, in particular,
using multiple wavelengths of light, but to date they have not been
accurate enough to allow for satisfactory CO measurement on actual
patients.
[0014] Invasive techniques have obvious disadvantages, the main one
of which is of course that catheterization of the heart is
potentially dangerous, especially considering that the subjects
(especially intensive care patients) on which it is performed are
often already in the hospital because of some actually or
potentially serious condition. Invasive methods also have less
obvious disadvantages: Some techniques such as thermodilution rely
on assumptions, such as uniform dispersion of the injected heat,
that affect the accuracy of the measurements depending on how well
they are fulfilled. Moreover, the very introduction of an
instrument into the blood flow may affect the value (for example,
flow rate) that the instrument measures.
[0015] There has therefore been a long-standing need for some way
of determining CO that is both non-invasive--or at least as
minimally invasive as possible--and accurate. One blood
characteristic that has proven particularly promising for
accurately determining CO non-invasively is blood pressure.
[0016] Most known blood-pressure-based systems rely on the
so-called pulse contour method (PCM), which calculates an estimate
of CO from characteristics of the beat-to-beat pressure waveform.
In the PCM, "Windkessel" (German for "air chamber") parameters
(characteristic impedance of the aorta, compliance, and total
peripheral resistance) are used to construct a linear or
non-linear, hemodynamic model of the aorta. In essence, blood flow
is analogized to a flow of electrical current in a circuit in which
an impedance is in series with a parallel-connected resistance and
capacitance (compliance).
[0017] FIG. 1 illustrates a classic two-element Windkessel model,
in which Q(t) is the flow of blood from the heart to the aorta (or
pulmonary artery); P(t) is the blood pressure in the aorta (or
pulmonary artery) at time t; C is arterial compliance; and R is
peripheral resistance in the systemic (or pulmonary) arterial
system, all in suitable units. Assuming that the entire flow Q(t)=Q
is constant and takes place only during systole, one obtains the
following expression for P(t) during systole:
P(t)=RQ-(RQ-P.sub.ed)e.sup.-t/.tau. (Equation 1) where P.sub.ed is
the end-diastolic pressure (diastolic pressure) and .tau.=RC is a
decay constant. During diastole, Q(t)=0 (no inflow) and the
expression for P(t) reduces to: P(t)=P.sub.ese.sup.-t/.tau.
(Equation 2) where P.sub.es is the end-systolic pressure.
[0018] The three required parameters of the model are usually
determined either empirically, through a complex calibration
process, or from compiled "anthropometric" data, that is, data
about the age, sex, height, weight, etc., of other patients or test
subjects. U.S. Pat. No. 5,400,793 (Wesseling, 28 Mar. 1995) and
U.S. Pat. No. 5,535,753 (Petrucelli, et al., 16 Jul. 1996) are
representative of systems that rely on a Windkessel circuit model
to determine CO.
[0019] Many extensions to the simple two-element Windkessel model
have been proposed in hopes of better accuracy. One such extension
was developed by the Swiss physiologists Broemser and Ranke in
their 1930 article "Ueber die Messung des Schlagvolumens des
Herzens auf unblutigem Weg," Zeitung fur Biologie 90 (1930)
467-507. FIG. 2 illustrates this model. In essence, the Broemser
model--also known as a three-element Windkessel model--adds a third
element (shown as resistance R0) to the basic two-element
Windkessel model to simulate resistance to blood flow due to the
aortic or pulmonary valve. It can be shown that the Broemser model
reduces to the basic two-element Windkessel model under either of
two circumstances: 1) R0=0; and 2) at diastole, when Q(t)=0 and
dQ(t)/dt=0. Windkessel models having even more elements than three
have also been proposed and analyzed.
[0020] PCM-based systems can monitor CO more or less continuously,
with no need for a catheter to be left in the patient. Indeed, some
PCM systems operate using blood pressure measurements taken using a
finger cuff. One drawback of PCM, however, is that it is no more
accurate than the rather simple, three-parameter model from which
it is derived; in general, a model of a much higher order would be
needed to faithfully account for other phenomena, such as the
complex pattern of pressure wave reflections due to multiple
impedance mis-matches caused by, for example, arterial branching.
Other improvements have therefore been proposed, with varying
degrees of complexity.
[0021] The "Method and Apparatus for Measuring Cardiac Output"
disclosed by Salvatore Romano in U.S. Pat. No. 6,758,822, for
example, represents a different attempt to improve upon PCM
techniques by estimating SV, either invasively or non-invasively,
as a function of the ratio between the area under the entire
pressure curve and a linear combination of various components of
impedance. In attempting to account for pressure reflections, the
Romano system relies not only on accurate estimates of inherently
noisy derivatives of the pressure function, but also on a series of
empirically determined, numerical adjustments to a mean pressure
value.
[0022] U.S. Published Patent Application No. 2004 0158163 (Richard
J. Cohen, et al., 12 Aug. 2004, "Methods and apparatus for
determining cardiac output") describes yet another technique for
determining CO from the pulse pressure profile P(t). According to
Cohen's method, the arterial blood pressure waveform (time profile)
P(t) is measured over more than one cardiac cycle. For example,
assume a pressure measurement taken over three cardiac cycles. The
area under the pressure curve is then computed for each cardiac
cycle. The pressure profile P(t) is also sampled ("digitized") to
form a sequence of discrete values y(j) that represent P(t).
[0023] As is well known, the impulse response of any system is the
function that describes how it acts (in reality or in a theoretical
model) when it is subjected to an impulse of energy, force, etc.
One step of Cohen's method involves creating a sequence of impulses
x(k)--one at the beginning of each cardiac cycle--that has the same
area as the "arterial pulse pressure." A second embodiment of
Cohen's method involves creating a sequence of impulses x(k), each
of which is located at the beginning of each cardiac cycle, with
impulses that have equal areas but that are independent of the
areas of the corresponding arterial pulse pressure waveforms. The
values of x(k) and y(j) are then used in a convolution computation
that models the cardiac system thus: y .function. ( k ) = i = 1 m
.times. a i y .function. ( k - i ) + i = 1 n .times. b i x
.function. ( k - i ) + e .function. ( k ) ( Equation .times.
.times. 3 ) ##EQU1## where e(t) is the residual error term, and m
and n limit the number of terms in the model. The set of
coefficients {a.sub.i, b.sub.i} that optimizes the equation is then
determined, for example, over 60-90 second intervals of x(k) and
y(j), and by using least-squares optimization to minimize the
residual error term e(t).
[0024] Given a.sub.i and b.sub.i, Cohen then derives a single
impulse response function h(t) that covers the entire multi-cycle
measurement interval. It has long been known that the impulse
response function of the heart usually takes the form,
approximately, of a first-order exponential decay function. After
an initial "settling" time of about 1.5-2.0 seconds, after which
the effects of pressure reflections have mostly died out, Cohen
then approximates h(t) from the expression: h .function. ( t ) = A
.times. .times. e - t .tau. D + w .function. ( t ) ( Equation
.times. .times. 4 ) ##EQU2## The parameters A (an assumed
amplitude) and .tau..sub.D (the time constant) are then estimated
from a minimization of the residual weight function w(t).
[0025] Cohen then computes CO, for example, from some variant of
the formula: CO=AC*ABP/.tau..sub.D (Equation 5) where AC is a
scaling constant and ABP is "arterial blood pressure," usually the
average arterial blood pressure. The scaling factor AC can be
determined using an independent calibration, and will either be, or
at least be related to the arterial compliance value C. This is
because, as is known: CO=MAP/R (Equation 6) where MAP is the mean
arterial pressure, which in most cases will be the same as Cohen's
term ABP. Equation 5 transforms into Equation 6 if AC=C, since
.tau..sub.D=R*C.
[0026] One weaknesses of the approach disclosed by Cohen is that it
requires determination of the scaling, that is, calibration factor
AC, or, equivalently, determination of C. Accuracy of the CO
measurement is therefore closely dependent on the accuracy of the
calibration or compliance calculation. Another weakness of Cohen's
method is that the recursive expression (Equation 3) used assumes a
constant input amplitude and therefore fails to determine the
proper d.c. offset. This in turn causes an even greater reliance on
accurate determination of AC (or C).
[0027] Still another disadvantage of Cohen's approach is that it
ignores much of the information contained in the pressure
waveform--indeed, one embodiment of Cohen's method uses only a
single characteristic of each waveform, namely, the area, when
constructing the impulses x(k). In a second embodiment of Cohen's
method, the information contained in the pulse pressure waveform is
totally ignored. Cohen compensates for this in part by evaluating
many pressure waveforms at a time--for example, Cohen's preferred
embodiment monitors CO by analyzing "long time scale variations
(greater than a cardiac cycle) in a single ABP signal" and
determines .tau..sub.D "through the analysis of long time
intervals" 60-90 seconds long. Another consequence of Cohen's
greatly simplified input signal x(t) is the need for a complicated
transfer function model (see Equation 3), which involves many
zeroes, many poles, and, consequently, design and computational
complexity.
[0028] What is needed is a system and method of operation for
estimating CO, or any parameter that can be derived from or using
CO, that is robust and accurate and that is less sensitive to
calibration errors. This invention meets this need, and, indeed,
provides an advantageous method and system for estimating even
other cardiovascular parameters.
SUMMARY OF THE INVENTION
[0029] The invention provides a processing system, and a related
method of operating it, for determining a cardiovascular parameter,
for example, cardiac output (CO), blood flow, stroke volume, or a
value that can be derived from any of these. A current pressure
waveform data set corresponding to arterial blood pressure is input
to the processing system over at least one current pressure cycle;
both invasive and non-invasive blood pressure-measuring devices may
be used. The defining parameters of an assumed, non-impulsive input
flow waveform are then determined as a function of a peripheral
resistance value determined for at least one previous pressure
cycle, at least one shape-characterizing value in the current
pressure waveform data, or both. For example, the defining
parameters may be computed so as to form a function that, when
transformed according to the cardiovascular model, most closely
yields the current pressure waveform data set in a predetermined
sense
[0030] One of several examples of a shape-characterizing value is
the time from the onset of systole to a time at or near systole,
which, in some embodiments of the invention, is used together with
the difference in pressure at these two times. The model parameters
of a flow-to-pressure cardiovascular model are also determined, if
they are not given. Examples of such a model include a discrete,
auto-regressive representation of a multi-element Windkessel model
of the aorta, in which case the model parameters are coefficients
of the discrete, auto-regressive representation. An estimate of the
cardiovascular parameter is then computed as a function of the
determined model parameters.
[0031] The assumed input flow waveform is advantageously a series
of assumed input waveform components. Examples of such waveform
components include square waves, saw tooth waves, polynomials,
piecewise linear functions, one or more Bezier curves, one or more
sinusoidal component curves, etc.
[0032] In one embodiment of the invention, in which the input flow
waveform components are determined as a function of a peripheral
resistance value, a diastolic time constant is estimated as a
product of a sampling rate at which the pressure waveform data set
is derived and a function of a model feedback parameter; an
arterial compliance value is estimated as a ratio of the diastolic
time constant and the peripheral resistance value; a systolic time
constant is estimated from chosen points in the current pressure
waveform data set; an aortic characteristic resistance value is
computed as a ratio of the systolic time constant and the arterial
compliance value; and the amplitude of the component waveform for
the current pressure cycle is set to be inversely proportional to
the square of a function of at least one aortic characteristic
resistance value.
[0033] In a particular version of this embodiment, the mean of a
plurality of aortic characteristic resistance values is computed,
which will include at least one aortic characteristic resistance
value estimated for a previous cycle, and the amplitude of the
component waveform for the current pressure cycle is set to be
inversely proportional to the square of the product of the mean and
a calibration constant and, optionally, the arterial compliance
value. Where the input waveform components are primarily
characterized by an amplitude and a duration, the amplitude of the
component waveform for the current pressure cycle may similarly be
set to be proportional to a peak-to-peak value of the current
pressure waveform data set and inversely proportional to a function
of the current peripheral resistance value, such as a mean value of
a plurality of previously estimated peripheral resistance values.
The amplitude may optionally be scaled by a calibration
constant.
[0034] In one embodiment, cardiac flow is estimated as a function
of the assumed input flow waveform. Cardiac stroke volume may then
be estimated by integrating the assumed input flow waveform over at
least one pressure cycle. The model parameters may be determined
either independently, or be predetermined or computed independent
of the current pressure waveform data set, or computed at the same
time as the defining parameters of the assumed input flow waveform
in a single optimization.
BRIEF DESCRIPTION OF THE DRAWINGS
[0035] FIG. 1 illustrates a two-element Windkessel model, which is
often used as the basis of the pulse contour method for estimating
cardiac output.
[0036] FIG. 2 illustrates the Broemser model, which is also known
as a three-element Windkessel model
[0037] FIG. 3 is an illustrative example of a complex blood
pressure curve over one beat-to-beat heart cycle.
[0038] FIG. 4 illustrates a discrete-time representation of the
pressure waveform in FIG. 3.
[0039] FIG. 5 illustrates the transfer function relationship
between flow and pressure in the arterial system.
[0040] FIG. 6 illustrates how an input flow signal (waveform) is
approximated as a sequence of input signal components derived from
a sensed pressure waveform.
[0041] FIG. 7 illustrates a switched three-element Windkessel model
used in one embodiment of the invention.
[0042] FIG. 8 illustrates how certain values are obtained from a
current pressure waveform for use in CO estimation using the
embodiment shown in FIG. 7.
[0043] FIG. 9 is a block diagram showing the main components of a
system according to the invention.
DETAILED DESCIRIPTION
[0044] In broadest terms, the invention involves a new pulse
contour method and system implementation for continuous assessment
of cardiac output (or of any value that can be derived from a
cardiac output estimate) from peripheral blood pressure. In
general, the invention posits an assumed, non-impulsive input flow
waveform, at least one of whose defining parameters is a function
of at least one value of an input pressure waveform data set, and
which is then used in a system-identification routine to determine
the parameters of a model of the relationship between input flow
and output pressure. Parameters characterizing the relationship are
then used to compute an estimate of the cardiovascular parameter of
interest.
[0045] The primary exemplifying embodiment of the invention
described below uses an autoregressive algorithm to compute values
of the arterial compliance and the peripheral resistance. The
invention then applies these values to the model as well. The
following discussion focuses primarily on the preferred embodiment
of the invention, since doing so also makes clear the important
generally applicable aspects of the invention, but various
alternatives are also described.
[0046] The invention may be used to advantage with any type of
subject, whether human or animal. Because it is anticipated that
the most common use of the invention will be on humans in a
diagnostic setting, the invention is described below primarily in
use with a "patient." This is by way of example only, however--it
is intended that the term "patient" should encompass all subjects,
both human and animal, regardless of setting.
[0047] Because of its clinical significance, it is anticipated that
most implementations of the invention will generate cardiac output
(CO) estimates--either as an end result or as an intermediate
result used for calculating for CO-related value--based on
measurements of systemic arterial blood pressure. It would also be
possible to use measurements of blood pressure taken elsewhere,
however, such as in the pulmonary artery on the right side,
although such sites may require invasive intracardiac measurement.
Moreover, another embodiment of the invention is described below in
which the (or another) cardiovascular value of interest is flow or
stroke volume, in which case there may be no need to calculate a CO
estimate at all, or to do so as a separate calculation.
[0048] The system according to one embodiment of invention
implements three main steps: 1) it generates an assumed input
waveform, which comprises a train of assumed input waveform
components, and which closely approximates the beat-by-beat blood
flow signal, which is preferably based on an acquired arterial
blood pressure signal and past estimated values of the arterial
compliance and the peripheral resistance; 2) it uses the generated
assumed input waveform and the acquired peripheral arterial pulse
pressure signal to estimate the arterial compliance and the
peripheral resistance with a system identification approach
relative to a model of the flow/pressure system; and 3) it uses the
estimated arterial compliance and peripheral resistance values to
generate the assumed input waveform component for the next time
interval and calculate a CO estimate.
[0049] Arterial compliance and peripheral resistance may thus be
estimated continuously based on a recursive system identification
approach, in which the current computed values are used to estimate
the blood flow of the next time interval. For the first time
interval at the start, reasonable initial values may be assumed.
Over the next time intervals, this embodiment of the invention
converges to the proper mean values of the arterial compliance and
the peripheral resistance. The invention enables continuous CO
monitoring from the peripheral blood pressure waveform.
[0050] Pressure Waveforms
[0051] FIG. 3 illustrates an example of a waveform P(t) of arterial
pressure taken over a single heart cycle, here, from the point of
diastolic pressure P.sub.dia at time t.sub.dia0, through the time
t.sub.sys of systolic pressure P.sub.sys, to a time t.sub.dial at
which the blood pressure once again reaches P.sub.dia.
[0052] According to the invention, P(t), or any signal that is
proportional to P(t), may be measured at any point in the arterial
tree, either invasively or non-invasively. If invasive instruments
are used, in particular, catheter-mounted pressure transducers,
then any artery may be used as a measurement point. Placement of
non-invasive transducers will typically be dictated by the
instruments themselves--the placement of finger cuffs, upper arm
pressure cuffs, and earlobe clamps should be obvious. Regardless of
the instrument, it will ultimately produce, or cause to be
produced, an electric signal corresponding (for example, equal or
just proportional) to P(t).
[0053] Rather than measure arterial blood pressure directly, any
other input signal may be used that is proportional to blood
pressure. Any needed scaling or conversion may then be done at any
or all of several points in the calculations described below. For
example, if some signal other than arterial blood pressure itself
is used as input, then it may be calibrated to blood pressure
before its values are used in the computations described below. In
short, the fact that the invention may in some cases use a
different input signal than a direct measurement of arterial blood
pressure does not limit its ability to generate an accurate CO
estimate. The only requirement of this invention is that a signal
or data set equal or at least having a known relationship to (such
as being proportional to) the patient's blood pressure over the
interval of interest (including continuously) must be made
available to the processing system (see below) that carries out the
signal conditioning and various calculations described below.
[0054] As is well known, and as is illustrated in FIG. 4, analog
signals such as P(t) can be digitized into a sequence of digital
values using any standard analog-to-digital converter (ADC) with a
sampling period of t.sub.s. In other words, P(t),
t0.ltoreq.t.ltoreq.tf, can be converted, using known methods and
circuitry, into the digital form P(k), k=0, (n-1), where t0 and tf
are initial and final times, respectively, of the computation
interval and n is the number of samples of P(t) to be included in
the calculations, distributed usually evenly over the computation
interval.
[0055] Two-Element Windkessel Embodiment
[0056] As mentioned above, the invention takes a system
identification approach relative to a model of the flow/pressure
system. Prototypes of the invention that use various Windkessel
models have been successfully tested, so the description of the
invention found here concentrates primarily on embodiments of the
invention that use system identification techniques based on
different versions of Windkessel modeling. The general method
according to the invention may be applied to implement many
different systems for estimating CO using other models as well,
however (including higher order models). The main requirement is
that the model can be reduced to a discrete transfer function with
parameters that can be determined through recursive comparison with
the input signal model described below.
[0057] A first embodiment of the invention is based on the simple
two-element resistance-capacitance electrical analog model of the
arterial system, that is, the simple Windkessel model shown in FIG.
1. Recall that, in this model, the arterial compliance is
represented by the capacitor C, and the peripheral resistance by
the resistor R. The blood flow is modeled by the current Q(t), and
the blood pressure P(t) is modeled by the voltage across the
resistor R.
[0058] To carry out computations numerically and to estimate blood
flow Q(t) (and subsequently CO) from the peripheral arterial pulse
pressure P(t), values for the model parameters C and R must be
known. The invention estimates the model parameters and the input
flow Q(t) simultaneously based on a parametric autoregressive
recursive approach.
[0059] The model shown in FIG. 1 has the following transfer
function T(s) (from flow to pressure) in the s-domain: T .function.
( s ) = R 1 + sRC ( Equation .times. .times. 7 ) ##EQU3##
[0060] Since the computations in a digital processing system are
performed on the digitized blood pressure signals (that is, P(k)
rather than directly on P(t)), the model must be converted to the
digital domain (z-domain). To convert the model from
continuous-time to discrete-time, the following approximation is
used: s .apprxeq. 1 - z - 1 t s ( Equation .times. .times. 8 )
##EQU4## where t.sub.s is the sampling interval.
[0061] Substituting Equation 8 into Equation 7 yields the following
discrete-time transfer function: H .function. ( z ) = R t s t s +
.tau. ( 1 1 - .tau. t s + .tau. z - 1 ) ( Equation .times. .times.
9 ) ##EQU5## where .tau.=RC.
[0062] The transfer function of Equation 9 can be approximated by a
first-order autoregressive model (AR model) having the following
form: H ^ .function. ( z ) = b 1 + a z - 1 ( Equation .times.
.times. 10 ) ##EQU6## The coefficient b thus represents a
feed-forward or d.c. gain factor and the coefficient a is a
feedback gain factor.
[0063] Note the simplicity of this transfer function model, which
has only a single pole, no zeroes, and corresponds to the "real
life" Windkessel model. Although the method of this invention is
not restricted to such a single-pole, no-zero transfer function
model, this illustrates that such simplicity is possible using the
invention, with accuracy that should be no less than that achieved
by Cohen, and possibly even better. The inventors hypothesize that
this is because the input model used in this invention incorporates
more information about each cycle of pressure waveform that just
its area.
[0064] The model coefficients a and b in Equation 10 can be
estimated using known parametric system identification methods. In
order to apply a system identification approach however, both the
input signal and the output signal of the system must be known.
Given the system's transfer function, such as Equation 10, and an
n'th estimate of the function's parameters (such as coefficients a
and b), system identification routines typically generate an output
signal (including waveforms) from the input signal and then compare
this output signal with the actual, observed output signal, and
either directly compute (if the function is simple enough) or, more
often, iteratively adjust the coefficients until the difference
between the generated and observed output signals is a minimum in
some quantitative sense. In other words, these routines compute the
values of the function's parameters that give a "best" match
between the generated and observed outputs in any known sense. The
coefficient values that give this best match are taken as the
(n+1)'th estimate. Accordingly, in FIG. 5, the discrete flow
(input) signal Q(k) is represented as waveform 50, the resulting
discrete pressure (output) signal P(k) is represented by waveform
54, and the transform function relating the two is shown as module
52.
[0065] It is preferable to avoid the need for both a pressure and a
flow transducer, however. Without actual knowledge of flow, only
the output (the blood pressure signal) is assumed to be available
to the system, with the system's input (blood flow) being
unknown.
[0066] For this reason, instead of using an actual measured blood
flow signal as the input for the system, the invention generates a
train of assumed input waveform components Q(i) that is assumed to
closely approximate it, with the time limits of each assumed input
waveform component being related to known points of the sensed
blood pressure waveform. The two key parameters in the construction
of an assumed input waveform component as illustrated in the
figures are its duration (the width) and its amplitude (the
height). Note that the assumed input waveform components are not
necessarily impulsive; in other words, each assumed input waveform
component is defined by at least two parameters, such as amplitude
and temporal width. Other parameters may include shape
characteristics (such as for a square wave, triangular waves such
as saw tooth waves, etc.); amplitude and frequency for each of a
set of Fourier components; the m+1 coefficients of a polynomial of
order m; the 8.times.n parameters of a set of n Bezier curves; the
endpoints (or just the x- or y-coordinates of the endpoints) of
segments of a piecewise linear approximating function, etc.
[0067] See FIG. 6. In the preferred two-element version of the
invention, the duration of each current assumed input waveform
component is set equal to the time interval between systole onset,
that is, at or near diastole P.sub.dia, and the location of the
peak value, that is, at or near systole P.sub.sys, of the pressure
waveform in the current beat. Thus, the three assumed input
waveform components Q(1), Q(2), and Q(3), in FIG. 6 extend
temporally from the times of d1, d2, d3 to the times of p1, p2, p3,
respectively.
[0068] According to Equation 7, the amplitude of the flow Q(t) is
related to the arterial pulse pressure by a gain factor of R;
therefore, the amplitude of the assumed input waveform,
Q.sub.max(t), is best estimated by multiplying the peak-to-peak
value of the arterial pulse pressure signal P.sub.max(t) by 1/R: Q
max .function. ( t ) = 1 R P max .function. ( t ) ( Equation
.times. .times. 11 ) ##EQU7##
[0069] To estimate the peripheral resistance R, the invention uses
a parametric system identification approach, in which the
coefficients a and b of Equation 10 are estimated using any known
technique, such as least mean square regression. As is known, the
way in which these routines work is to measure the difference
between the observed output (pressure) waveform and the output
(pressure) waveform that is produced by applying the transfer
function with given parameters (a and b coefficients) to the
assumed input waveform (Q(i)). The routine then iteratively
(usually) adjusts the coefficients until a "best" fit is found
according to some metric, such as least squares.
[0070] The input and the output of the system being identified are,
respectively, the train of assumed input waveform components Q(i),
which is taken to be an approximation of the flow signal Q(t), and
the measured arterial pulse pressure P(t) (or, rather, its
representation P(k)). Once the coefficients a and b are estimated,
the invention can then calculate vascular resistance as follows: R
= t s + .tau. t s b ( Equation .times. .times. 12 ) ##EQU8## where
the time constant .tau. is estimated using the following equation:
.tau. = a 1 - a t s ( Equation .times. .times. 13 ) ##EQU9##
[0071] The value of the peripheral resistance changes slowly from
beat to beat; consequently, it will normally suffice to use a
single value of R for an entire measurement interval of, for
example, 15 or 30 s. The invention estimates R continuously, using
a recursive approach: The current computed value of R is used to
estimate the amplitude of each assumed input waveform component
Q(i,k) in the train of assumed input waveform components Q(i) over
the next time interval, and so on. The train of assumed input
waveform components Q(i) is then used as the input for the system
identification routine, which estimates the new coefficients a and
b of the transfer function and therefore the new value of R. For
the first time interval, that is, initially, any reasonable initial
value of R may be assumed, and can be selected based on known
properties of R, determined using well known laboratory methods, or
in any other known manner. Over subsequent time intervals, the
method converges to the proper value of R. For practical
considerations, to reduce the effect of any variation in R and to
ensure stability, instead of the previous value of R, the mean
value of the N last time intervals may be used instead. Thus, for
the n-th assumed input waveform, the amplitude of each waveform
component Q(n,k) is estimated as follows: Q max .function. ( n , k
) = 1 k r 1 N .times. p = n - N - 1 p = n - 1 .times. R .function.
( p ) P max .function. ( n , k ) ( Equation .times. .times. 14 )
##EQU10## where k.sub.r is a constant reflecting the inaccuracies
and the deviation of the assumed first-order AR model from the real
arterial system.
[0072] So, at each iteration, the invention computes Q.sub.max(i,k)
for each assumed input waveform component using the mean value of
the N past values of R. Then, the train of assumed input waveform
components Q(i) is generated with components having respective
amplitudes Q.sub.max(i,k). The train of assumed input waveform
components is then used to estimate the current value of R, for
example, by using the approach of least-mean-square system
identification applied to the model described by Equation 10. A CO
value can then be computed using the well known formula: CO=MAP/R
(Equation 15) where MAP is the mean arterial pressure and R is the
current value of the peripheral resistance. MAP may be computed in
any known way, for example, by taking the average of P(k) values
over one or more cardiac cycles (that is, over one or more
trough-to-trough or other periods of the discrete pressure waveform
P(k)).
[0073] Notice that the invention estimates CO without needing to
directly measure the model input signal, that is, the flow, and
without needing to determine a compliance value C. Rather, an
assumed input signal is used, and C is implicit in the time
constant .tau., which itself is implicit in the recursively
estimated model coefficients a and b.
[0074] As illustrated in FIG. 6, each assumed input waveform
component Q(i) is a simple square-wave. This has the advantage of
computational simplicity and has proven in tests to be adequate.
Moreover, even the square-wave assumed input waveform components
described above contain information not only about the values and
times of systole onset and peak pressure of the current waveform,
but also of previous values of R; thus, compared with Cohen, the
invention's assumed input waveform components encode much more
information, and thus can rely on a less complicated (even
single-pole, if desired) transfer function model.
[0075] A square-wave input signal is not necessary to the
invention, however. Rather, other assumed input waveform component
shapes could be used that more closely approximate the known
profile of flow, such as is illustrated roughly in box 50 of FIG.
5. For example, a saw-tooth assumed input waveform component, full
or half parabola, full or half sine wave, a composite sinusoidal
waveform derived by Fourier analysis from know flow profiles, a
polynomial approximation, etc., might better match the area under
the portion of the flow waveform that corresponds to the time
interval from the time of d1 to the time of p1. If such other
assumed input waveform components are used, then skilled
programmers, especially those with a background in numerical
analysis and the design of time-series parameter identification
methods, will know how to adjust the various optimization
algorithms accordingly, for example, by including additional
parameters relating, for example, to the shape or number of
components in the approximating function for flow.
[0076] It would also be possible to perform the computations
described here using the data from the input pressure waveform data
set extending over more than one pressure cycle and, for example,
to determine more than one assumed input waveform component at a
time. Moreover, each assumed input waveform component could also be
determined such that it is "wider" than what is illustrated in FIG.
6, that is, it need not end at the time at or near systole
P.sub.sys, but might even extend longer, even over each full
cycle.
[0077] Three-Element Windkessel Embodiment
[0078] The second version of the method is based on the
three-element analog model of the arterial system shown in FIG. 2.
As explained above, the three elements of this model represent the
three basic properties of the arterial system: R0--aortic
characteristic resistance; C--vascular compliance; and
R--peripheral resistance. As shown in FIG. 7, however, the model of
the arterial system used in this embodiment of the invention also
includes a single pole, double-throw switch SW in series between
the resistance RO, and the parallel-connected capacitor C and
resistance R. When the switch is in a first position (labeled 1),
the capacitor C is charged by the current (aortic systolic inflow)
Q.sub.s(t)(=Q(t)) through the resistance R0. When the switch is in
a second position, the capacitor C discharges with current
(diastolic outflow) Q.sub.d(t) through the resistance R.
[0079] As in the two-element embodiment of the invention described
above, to compute the input flow from the arterial pulse pressure,
it is first necessary to estimate the values of the model
parameters R0, C and R, either directly or implicitly. As did
Wesseling this embodiment of the invention builds on the following
assumptions: during systole (switch SW in position 1, the aortic
systolic inflow (Q.sub.s) is principally determined by the time
constant .tau..sub.s=R0 C: the peripheral resistance R is not a
major determinant of systolic inflow. During diastole (switch SW in
position 2), this inflow is dissipated in the periphery. The
diastolic outflow Q.sub.d and the pressure decay are essentially
determined by the time constant .tau..sub.d=R C. The compliance C
is a common parameter in both time constants. This assumption is
reasonable because it reflects the actual vascular physiological
parameters: during systole the ventricle ejects blood into the
compliant aorta. This blood is stored in systole, and, on elastic
recoil in diastole, the peripheral vessels are perfused. In order
to estimate the model's parameters R0, C and R the following
approach is used:
[0080] In this aspect of the invention, the peripheral resistance R
and the system's time constant .tau. are first estimated using the
model of FIG. 1 and the recursive system identification routine
described above (Equations 12 and 13) is executed. This is possible
to do because, from the system identification point of view, the
effect of R C is significantly greater than the effect of R0 C.
This means that the time constant .tau..sub.d during diastole is
significantly greater than the time constant .tau..sub.s during
systole. Therefore, the results of the system identification
estimation will reflect mainly the effects of R and C and the time
constant .tau. estimated using system identification and Equation
13 is in fact the time constant during diastole .tau..sub.d: .tau.
d = a 1 - a t S ( Equation .times. .times. 16 ) ##EQU11##
[0081] In this case, the peripheral resistance would be: R = t S +
.tau. d t S b ( Equation .times. .times. 17 ) ##EQU12##
[0082] The train of assumed input waveform components needed for
system identification is generated using a similar approach as
before: Each assumed input waveform component Q(i,k) is located at
the start of a systole of the blood pressure waveform and its width
is set equal to the time interval between the systole onset and the
location of the peak value of the pressure waveform in the current
beat (between points di and pi in FIG. 6). The height (amplitude)
of the component is defined by the three-element electrical model
when the switch SW is in position 1 (FIG. 7): Q max .function. ( t
) = 1 ( R .times. .times. 0 C ) 2 P max .function. ( t ) ( Equation
.times. .times. 18 ) ##EQU13##
[0083] In order to estimate R0, the invention uses the following
approach: First the compliance C is estimated, using Equations 16
and 17: C = .tau. d R ( Equation .times. .times. 19 ) ##EQU14##
[0084] R0 is then calculated: R .times. .times. 0 = .tau. s C (
Equation .times. .times. 20 ) ##EQU15##
[0085] The systolic time constant .tau..sub.s is estimated by
selecting two points on the rising edge of the arterial pulse
pressure waveform (for example, at 30% and 70% of the diastole
level, respectively) as illustrated in FIG. 8, and then applying
any known optimization routine to minimize the following function:
min .tau. s .times. ( P 1 - P 2 = P 1 .times. e t 2 .tau. s - P 2
.times. e t 1 .tau. s ) ( Equation .times. .times. 21 )
##EQU16##
[0086] As in the previous case, the amplitudes Q.sub.max(i,k) of
the individual assumed input waveform components are estimated
using the mean value of R0 over the N last time intervals: Q max
.function. ( n , k ) = 1 ( k r 1 N C .times. p = n - N - 1 p = n -
1 .times. R .times. .times. 0 .times. ( p ) ) 2 P max .function. (
n , k ) ( Equation .times. .times. 22 ) ##EQU17##
[0087] Cardiac output CO may then be calculated as before, that is,
as in Equation 15.
[0088] Calibration
[0089] Both embodiments of the invention described above ultimately
assume a determination of the k.sub.r constant in Equations 14 and
22. This is a calibration constant, which reflects the inaccuracies
and the deviations due to the presumed first-order AR models of the
arterial system.
[0090] The calibration constant k.sub.r could be estimated using,
for example, a CO value measured by a bolus injection or any other
"gold standard" method. In this case, the calibration could be done
once for the current subject/patient at the start of the recording,
and could remain effective for a long time afterward. Such
embodiments of the invention can be termed "with-caf" embodiments
in that they are provided with a value of k.sub.r that is obtained
through external calibration. Experimental results and clinical
studies using the invention show that the "with-cal" version of the
algorithm offers both high accuracy and a very good trending of the
estimated cardiac output.
[0091] As Equations 14 and 22 show, the calibration constant
k.sub.r is within the recursion and therefore is affected by the
feedback. The fact that calibration is done in the feedback loop,
within the recursion and within the averaging, makes the algorithm
less sensitive to the errors in the estimation of the calibration
constant. In fact, the inventors have demonstrated experimentally
that the error in the estimated CO value is proportional to the
square root of the error in k.sub.r. For instance, if the estimated
k.sub.r deviates by 30% from the actual k.sub.r, then this will
cause a deviation of only 5.5% in the estimated cardiac output.
This makes the invention more appropriate to use in either a
"with-cal" or a "no-cal" mode than are purely linear methods.
[0092] Here, the "no-cal" mode is, as its name implies, simply a
mode of operation of the invention in which no empirically
determined, patient-specific value of k.sub.r is supplied at all.
This would eliminate the need for external calibration. In such
cases, k.sub.r could be set either simply to unity, or it could be
set to an value pre-determined experimentally on, for example, a
representative population of subjects, or of a population of
subjects representative in some way (such as with respect to age,
weight, sex, pathology, etc.) of the current subject/patient.
[0093] Another advantage of the invention is that a benefit of the
square-root error dependence is that it is possible to use an
averaged calibration constant for a whole population under study.
For example, in tests, the inventors were able to use a k.sub.r
value of 1.4, and yet were able to keep the DC-shift (offset) error
under 30% for 85% of the patients. Also, the inventors also propose
that noninvasive methods such as ECG and bioimpedance may be used
to estimate k.sub.r; even in such cases, the recursive nature of
the invention makes it more appropriate than prior art systems,
since it is less sensitive to any error in the calibration constant
estimation.
[0094] Advantages
[0095] The invention displays several advantages over the prior
art. Some advantages are mentioned above; others include:
[0096] a) High accuracy: Results on animal and clinical radial and
femoral data show that the invention offers significantly higher
accuracy when compared with competing devices.
[0097] b) Improved trending: Results on animal radial and femoral
data show that changes in the peripheral resistance, for example
after vasodilation or vasoconstriction, are well reflected in the
estimated CO trends.
[0098] c) The invention may be used in a "no-cal" mode, that is,
with no a priori value of the calibration constant k.sub.r
available.
[0099] d) In the "no-cal" mode, the invention works well even if an
average calibration constant is used (within 30% error in 85% of
the cases). The accuracy of the "no-cal" mode of the invention can
be improved, however, if the calibration constant k.sub.r is
estimated using a third parameter: In an animal study, the
inventors were able to show that the slope of the rising edge of
the blood pressure waveform can be used to group the animals by
their calibration constants. The inventors propose that this
technique may also be used on humans, such that the calibration
constant of each patient's group is used for that patient according
to the characteristics of the group, such as age, body mass, sex,
etc., that is, standard anthropometric characteristics. Also, a
third measurement could be used to estimate the calibration
constant; this measurement could be based on different techniques,
such as EKG (QRS--Systole onset interval) and bioimpedance
(Volume--Compliance relation).
[0100] e) The method according to the invention is computationally
simpler than other existing pulse contour methods. For example,
there is no need to detect the dicrotic notch in the blood pressure
waveform, which makes the invention more stable and less sensitive
to errors, noise and motion artifacts.
[0101] f) The invention is able to estimate peripheral resistance R
directly, with no need to derive it indirectly from the decay
constant .tau.. This is a useful property in applications that
estimate cardiovascular parameters other than, or in addition to
CO, based on R. Indeed, since R has clinical significance of its
own, the aspects of the invention described above relating to the
estimation of R may be all that are needed in some cases.
[0102] System Components
[0103] FIG. 9 shows the main components of a system that implements
the method described above for sensing pressure and calculating CO
according to the invention. The invention may be included within an
existing patient-monitoring device, or it may be implemented as a
dedicated monitor. As is mentioned above, pressure, or some other
input signal proportional to pressure, may be sensed in either or,
indeed, both, of two ways: invasively and non-invasively. Simply
because it is anticipated to be the most common implementation of
the invention, the system is described as measuring arterial blood
pressure as opposed to some other input signal that is converted to
pressure.
[0104] FIG. 9 shows both types of pressure sensing for the sake of
conciseness; in most practical applications of the invention,
either one or several variations will typically be implemented. In
invasive applications of the invention, a conventional pressure
sensor 100 is mounted on a catheter 110, which is inserted in an
artery 120 of a portion 130 of the body of a human or animal
patient. Such artery could be an ascending aorta, or pulmonary
artery, or, in order to reduce the level of invasiveness, the
artery 120 could be peripheral, such as the femoral, radial or
brachial artery. In the non-invasive applications of the invention,
a conventional pressure sensor 200, such as a
photo-plethysmographic blood pressure probe, is mounted externally
in any conventional manner, for example using a cuff around a
finger 230 or a transducer mounted on the wrist of the patient.
FIG. 9 schematically shows both types.
[0105] The signals from the sensors 100, 200 are passed via any
known connectors as inputs to a processing system 300, which
includes one or more processors 350 and other supporting hardware,
such as a memory 301, and system software (not shown) usually
included to process signals and execute code. The invention may be
implemented using a modified, standard, personal computer, or it
may be incorporated into a larger, specialized monitoring system.
In this invention, the processing system 300 also may include, or
is connected to, conditioning circuitry 302 which performs such
normal signal processing tasks as amplification, filtering,
ranging, etc., as needed.
[0106] The conditioned, sensed input pressure signal P(t) is then
converted to digital form by a conventional analog-to-digital
converter ADC 304, which has or takes its time reference from a
clock circuit 305. As is well understood, the sampling frequency of
the ADC 304 should be chosen with regard to the Nyquist criterion
so as to avoid aliasing of the pressure signal; this procedure is
very well known in the art of digital signal processing. The output
from the ADC 304 will be a discrete representation of the pressure
signal P(t), whose sampled values may be stored in conventional
memory circuitry (not shown).
[0107] A signal pre-processing module 306 is preferably included,
with routines to provide such known pre-processing as digital
filtering for general (as opposed to interval-to-interval) noise
removal, for motion artifact rejection, pulse beat detection (if
needed), for rejection of bad beats, etc. This module may also be
implemented wholly or partially in hardware. Known circuitry may be
included to indicate, for example, that signal strength is too low,
and that the delivered measurement values are unreliable. As such,
the module 306 may also be located functionally, wholly or
partially, before the ADC 304. The output from the module 306 is
shown as P(k), since, if the pre-processing module 306 is included
at all its values will form the data set corresponding to pressure
that is used in the computations described above.
[0108] The values P(k) are passed (usually, accessed from memory
by) to a software module 310 comprising computer-executable code
for determining the pressure and time parameters used in the
computations for the chosen model. For the two-element model
described above, these will be the maximum pressure value
P.sub.max, pi and di; for the three-element model, P1, P2, t1 and
t2 are determined.
[0109] Yet another module 311 computes the mean arterial pressure
MAP over the chosen computation interval such as a cardiac cycle,
which may be triggered by any known hardware device and/or software
routine 340 that detects heart rate or at least signals the
beginning of a cardiac cycle. Note that the embodiments of the
invention described above do not strictly require any information
about the beginning and end of pressure waveforms during a
computation interval other that what can be derived from the
pressure waveforms themselves. The heart rate monitoring routine or
device is therefore optional, although it may be helpful as a way
to check that the pressure waveforms are correctly delimited.
[0110] Once the values of P.sub.max, pi and di are available from
the current pressure waveform, that is, for the current cardiac
cycle, the corresponding current assumed input waveform component
Q(i,k) can be generated as described above and added to the train
of assumed input waveform components. A module 312 is illustrated
in FIG. 9 that generates the assumed input waveform components.
[0111] A system parameter identification module 313 takes the
discrete pressure waveform P(k) and the train of assumed input
waveform components Q(i) as inputs. As described above, this module
computes the coefficients a and b that over each cardiac cycle,
yield a transfer function that best generates the observed pressure
signal P(t) in any chosen sense, such as least squares.
[0112] Once the coefficients a and b are computed, they are passed
as input parameters to another module 315, which calculates a value
of R and, depending on the implemented embodiment, also
.tau..sub.s. The value of R (and of TS if needed) is passed both to
the assumed input waveform component generation (or, more
generally, the input flow waveform) module 312, and to another
module 330 that performs the calculations indicated above for
computing the cardiovascular value of interest, such as a CO value,
a value that is derived from CO, etc. Yet another module 316--which
will in most cases simply be a memory position--provides to the
module 312 the calibration constant k.sub.r, which may be
determined as described above.
[0113] Software modules 310, 311, 312, 313, 315, 316 and 330 can be
programmed using known techniques. Of course, any or all of these
modules may be combined, even into a single body of code; they are
shown separately for the sake of clarity. Indeed, any or all of the
illustrated modules may be implemented simply as routines within a
single estimation software component 370, which may of course be
combined with other software components of the processing system
300 as desired. Moreover, any or all of the software components of
the invention may also be stored as computer-executable
instructions on any form of computer-readable medium (CD ROM,
memory or disk space made available for downloading, etc.) for
loading into and execution by different processing systems.
[0114] Once a CO estimate has been computed, it is passed to any
desired output device 500, such as a user-viewable monitor, and
displayed, stored or transmitted in any chosen format. An input
device 400 is preferably also included to allow the user to input,
for example, the calibration constant k.sub.r, administrative and
patient-specific information, to adjust the display, to choose the
computation interval, etc.
[0115] Dynamically Constructed Assumed Flow Input Waveforms
[0116] It has been mentioned above that the assumed input flow
waveform Q(i) need not be a square wave, but rather could be some
other shape whose amplitude and duration are adjusted according to
the current pressure waveform. It would also be possible to posit,
for each pressure cycle, an input flow waveform whose shape is more
generally adjustable, with shape parameters that are determined as
part of the optimization inherent in the system identification
procedure. In other words, parameters defining the shape of each
assumed input waveform component could be included, along with the
parameters defining the model of the relationship (such as the
transform function) between the assumed input flow waveform and the
current pressure waveform data set, as optimization parameters of a
single identification routine. The parameters of both may then be
determined simultaneously to yield both an optimal assumed input
flow waveform and an optimal model as defined according to any
chosen metric, such as least squares.
[0117] The approximate shape of a typical beat-to-beat flow profile
is known. See, for example, box 50 in FIG. 5, which illustrates a
characteristic flow waveform. As just one example, an initial
"generic" flow waveform Q(i,0) could be defined as a discrete
(sampled) representation of the parabola Q(t)=c2*x.sup.2+c1*x+c0
where x=[t-(t.sub.sys-offset)], that is, time measured relative to
the time of maximum pressure. The parameters c2 (which will usually
be negative), c1, c0 and even offset could then be included as four
of six optimization parameters in the system identification routine
used also to estimate optimal a and b values in the transfer
function model.
[0118] The result of the numerical optimization will then be
parameters defining not only optimal a and b values, but also the
parameters defining an optimal parabolic approximation of the input
flow waveform. In other words, by relaxing the assumption of a
fixed flow waveform shape (such as square-wave with a duration and
amplitude defined before system identification) even further, the
invention would thus determine not only which transfer function but
also which input waveform (not necessarily parabolic) most likely
(in the sense of any chosen metric, such as least squares) has led
to the observed pressure waveform. Integrating over the
approximated input flow waveform may then provide an estimate of
total flow over the pressure cycle.
[0119] Other approximating functions for input flow could of course
also be determined in this manner. For example, a higher order
polynomial could be used. As yet another example, the initial input
flow waveform could be assumed to be a set of Bezier curves, such
that the positions of each curve's two endpoints and two control
points (for a total of eight optimization parameters per curve)
could be made parameters that are computed in the optimization step
of the system identification routine. Yet another example would be
the amplitudes of component sine waves pre-determined initially
through Fourier analysis of representative, actually measured input
flow waveforms. Still other approximating functions will of course
occur to those skilled in the art of system identification and
reconstruction techniques.
[0120] It would even be possible to use the method according to the
invention primarily to determine an optimal functional
approximation of flow: Assume that one has in some other way (or
even using the invention over earlier cycles) determined the
parameters defining the transfer function model of the pressure
response P(t) to input flow Q(t). For example, one may have
determined the parameters of an n-element aortic Windkessel model
that one assumes to be accurate enough. The parameters defining the
general shape (such as polynomial, sinusoidal, piecewise linear,
etc.) of an assumed input flow could then be optimized using the
system-identification procedure described above. For each cycle or
group of cycles, the specific shape of an optimum input flow model
(that is, function) would then be determined even without
simultaneous optimization or adjustment of any transfer function
model coefficients at all. Cardiac flow may then be estimated from
the assumed input flow waveform, either directly or possibly after
scaling; any needed scaling may be determined using known
methods.
[0121] Knowledge of a flow model may be useful in its own right,
but may also be combined with other information to provide other
diagnostic indicators. For example, integrating the assumed input
flow waveform over a cardiac cycle will yield an estimate of
cardiac stroke volume (SV). Note that this estimate of SV does not
require knowledge of arterial diameter or cross-sectional area as
many other SV-estimating systems do.
* * * * *